Answer:
226 ft²
Step-by-step explanation:
The surface of the figure can be considered in several parts:
a) top and bottom surfaces
b) outside surfaces
c) inside surfaces
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The top and bottom surfaces each consist of a rectangle 8 ft by 4 ft with a 4 ft by 1 ft hole. The area of the larger rectangle without the hole is the product of its length and width:
(8 ft)(4 ft) = 32 ft²
The area of the hole is the product of its length and width:
(4 ft)(1 ft) = 4 ft²
Then the area of the surface around the hole is the difference of these:
32 ft² - 4 ft² = 28 ft²
The top and bottom surfaces together have twice this area for a total of ...
top and bottom area = 2·(28 ft²) = 56 ft²
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The outside (lateral) area is the total area of the four rectangles that make up the sides of the figure. Each rectangle has a height of 5 ft, so we can compute the area by finding the perimeter of the figure and multiplying that by 5 ft.
The perimeter is the sum of the lengths of its top or bottom edges:
8 ft + 4 ft + 8 ft + 4 ft = 2·(8 ft +4 ft) = 2·12 ft = 24 ft
Then the lateral area is ...
outside lateral area = (5 ft)(24 ft) = 120 ft²
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The area of the sides of the hole can be computed the same way. The hole is 5 ft high and its edge lengths are 1 ft and 4 ft. Then the total inside lateral area is ...
inside lateral area = (5 ft)(2·(1 ft + 4ft)) = 50 ft²
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So the total surface area of the solid is ...
total area = top and bottom area + outside lateral area + inside lateral area
total area = (56 + 120 + 50) ft²
total area = 226 ft²
